∫dx/[x^3(ax^2+b)]=-0.5∫1/(ax^2+b)d(x^-2)
令x^-2=t
则原式=-0.5∫t/(a+bt)dt=-0.5∫(1/b-a/(ab+b^2×t))dt
于是积分可得原式=-t/2b+(a/b^2)×ln(ab+b^2×t)+c
=-1/(2bx^2)+a/(2b^2)×ln(a+b/x^2)+c
∫dx/[x^3(ax^2+b)]=-0.5∫1/(ax^2+b)d(x^-2)
令x^-2=t
则原式=-0.5∫t/(a+bt)dt=-0.5∫(1/b-a/(ab+b^2×t))dt
于是积分可得原式=-t/2b+(a/b^2)×ln(ab+b^2×t)+c
=-1/(2bx^2)+a/(2b^2)×ln(a+b/x^2)+c